In standard axiomatic set theory, by the principle of extensionality, two sets are equal if they have the same elements (that is, neither of them has an element not in the other). As a result, there can be only one set with no elements, hence the usage of "the empty set" rather than "an empty set".

citation

Wikipedia contributors. (2023, October 28). Empty set. In Wikipedia, The Free Encyclopedia. Retrieved October 31, 2023, from https://en.wikipedia.org/w/index.php?title=Empty_set&oldid=1182337108

Alpheratz (stars.astro.illinois.edu) ALPHERATZ (Alpha Andromedae). Andromeda runs like a string of pearls to the northeast of the Great Square of Pegasus. Since its three principal stars have almost the same brightness, Beyer simply lettered them Alpha, Beta, and Gamma in order, Alpha and Beta tied for the lead in apparent magnitude. Mid-second magnitude (2.06) Alpheratz, the Alpha star, connects Andromeda (the Lady) with Pegasus, the Flying Horse that carried Perseus to Andromeda’s rescue.

Empty set (Wikipedia) In mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the empty set.